The Rydberg atom in time-dependent homogeneous electric and magnetic fields

Time evolution of the hydrogen-like Rydberg atom placed in homogeneous electric and magnetic fields with an arbitrary time dependence is considered. Within the manifold of the electron states with the same principal quantum number n, the problem is effectively reduced to the solution of two independent two-state problems. In particular, this reduction allows us to use in the analysis exactly solvable two-state models which are well known in the collision theory. As an example, we consider the case of perpendicular space-fixed fields; the magnetic field remains constant whereas the electric field strength varies linearly with time. The effective two-state problem corresponds to the well known Landau - Zener model. The simple formulae are obtained for the final population of Rydberg states. In the case of time-periodic fields the general properties of the quasienergy spectrum are established.